SPESPE 14207

Estimation of theGas Wells

Coefficient

by R. Noman, /mperia/ C.; N. Shrimanker,

SPE Members

of Inertial Resistance in High-Rate

British Gas Corp.; and J.S. Archer, /mperia/ C.

Copyright 19S5, Society of Petroleum Engineers

This paper was prepared for vreaantatkm at the SOth Annual Technical Conference and Exhibition of the Society of Petroleum Engineers held in Laa

Vegas, NV September 22-25, 1985.

This paper waa selected for presentation by an SPE Program Comminee following review of information contained in an abstract submitted by theauthor(s). Contents of the paper, aa presented, have not been reviewad by the Society of Petroleum Engineera and are subject 10 correction by theauthor(e). The material, as presented, does not necessarily reflect any pesifion of the Society of Petroleum Engineers, its onlcera, or members. Paparspresented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy iareetriofad to an abstract of not more thsn 300 words. Illustrations may not be copied. The abetracf should contain conapicuoua acknowledgment of wheraand by whom the paper is presented. Write Publications Manager, SPE, PO. eox 833S36, Richardson, TX 750S3-3S36. Telex, 730989 SPEDAL.

ABSTRACT‘ihe value of p can be estimated from laboratory

The pressure drop due to non-Dsrcy flow in a gas weii measurements on core piugs and from mliiti-~at~producing at high rates can be determined from analysis pressure tests conducted in a well. Correlationsof multi-rate pressure test data. In the absence of published in the literature have all rmde use ofsuch data calculation of the non-Darcy term requires a the first method, and are often found to predictknowle~e of the coefficient of inertiai resistance. flow behaviour with unacceptable accuracy.

This paper presents correlations for estimating the In this work the second method has been used tocoefficient of inertial resistance from reservoir calculate P and experimental measurements on coreporosity, permeability and gas saturation. These plugs were also carried out for comparison. Thecorrelations were derived from analysis of multi-rate ~-factors obtained have then been correlated withpressure tests conducted in over one hundred gas walis available reservoir parameters. The empiricaland are supported by experimental data using core correlations obtained by this method could be usedplugs. They are found to be better than other in predicting the non-lhrcy pressure drop for otherpublished relationships in predicting observed wells where, due to reservoir or operationalperformance. constraints it may be difficult to conduct any

extended nmlti-rate flow test.INTRODUCTION

It is well known that deviation from Darcy% isw occursfor fluid flow through porous media at high velocity.

-IALAK)~~

This phenomena is especially significant in the region In the early literature it was supposed that fluidsurrounding the wellbore of a gas well producing athigh rate.

flowi~ at high velocity through porous media wouldbehave like a fluid flowing through a conduit and

In this situation the Forchheimer equationl CM providesuffer energy loss from turbulence. Thecoefficient p

a better description of flow than Darcyts law. Thewas therefore often termed

Forchheimer equation may be represented by“turbulence factor” . More recently it has becaneclear that turbulence does not play any significant

*part on flow behaviour of interest in reservoir~inaering, and that the deviation from Darcy’s

—— = a pv+ /3Pv2 (1) law is the result of:dL

a) the convective acceleration and deceleration

where a is the coefficient of viscous flow resistanceof fluid particles as they travel through the

(=1/k). The term P is generallpores2, and

# known as thecoefficient of inertial resistance although other b) the displacement of fluid particles from anames have been proposed in the literature. l%e straight line due to the tortuous path in asecond term in this equation represents the- extra-- porous media3.pressure drop caused by the high flow rate.

References and illustrations at endof paper.

2 Inertial Coefficient in High Rate Gas Wells SPE 14207

NKKlU3AlWD~ICN~)

Dimensional consideration of Eqn 1 shcxvs that a ,the viscous coefficient has dimension of [L2] andP, the inertial coefficient has dimension [L-ll.

~ese two coefficients are independent of the fluidproperties and since both have the dimensions oflength they are expected to contribute to thecharacterisation of the structure of the porousmediun.

Numerous attempts have been made in the literatureto derive the Forchheimer equation fran theoreticalconsiderations, and attribute significance to thecoefficients. l%ese shmv that P canbe related invarious ways to porosity, permeability, tortuosity,specific surface area, size distribution of grainsand pores, surface-~eughness etc.

It would seem that each of these attenpts are validonly for the specific conditions for which theywere derived and no universally applicablerelationship has emerged. Green and Duwez5 forexample mention that “ /3 might represent aresistance equivalent to a certain number ofcontractions and expansions per unit length of thepath”.

Mny Qf the cQrrelatioIM proposed in the literaturewhich express ~ in terms of permeability andporosity are dimensionally incorrect, and requirethe units to be specified. Geertsme2 proposed a-dimensionally correct relationship between # , kand P . The arguments used in proposing thisrelationship are valid for unconsolidated sands.For consolidated rocks such relationships are notnecessarily valid and the application of Geertsmatsequation has been found to give very erroneousresults in many instances.

In the present study we have also sought torelate # from well tests to porosity andpermeability and have obtained correlations whichgive results better than other known relations. ofnecessity some of these relations are alsodimensionally inhanogenous. Fractional dimensionshowever may be reasonable in the description ofporous media6.

Until the true nature of the ~-factor is betterunderstood it will be necessary to rely on theseempirical correlations, since they are adequate formost engineering calculations.

WMxREmmm /3 Fmdm’nsrs

Using the real gas pseudo pressure, the inflowequation for a gas well rmy be written as

m(p) - m(~f) = AQ+BQ2 (2)

where A is the Darcy coefficient and for a semisteady state flow may be represented in oil field

units by

IA99 T i ‘e ~ \A=-

(h — -— +s

)

(3)kh rw 4

In Eqn. 2, B is the non-Darcy term and can be foundfran

k-k) ‘4)3.161x10-12 PTP 1

B=~ h2

Since, in general, I/re is negligible ccnpared tol/rw, I@ 4may be simplified to

3.161x10-12 /3TvB= (5)

~h2 rw

Fran a multi-rate pressure test, the apparent skinS’ can be calculated for each rate of production.‘lhe apparant skinS’ is related to the flowrate by

S1 = S+@ (6)

whereD= Bkh

1422T (7)

A plot of S’ against Qfrunndti-rate drawdmvn canbe.used to Obtfin the value of S as the interceptend D as the gradient, according to Eqn.6.

me value of B can therefore be found from Eqn.7since D is already known, and hence the valueof P can be evaluated from Eqn. 5 for theparticular well.

Excepting for a few cases, all the pressure test~.t. .~me.f~ hm~~ WtWP rmalv~ed USing the real gas“CZ.Q1-F . ..,” -----pseudo pressure and--~~~E&d of superposition7.

ixrr —us

Data from wireline logs and isochronal orflmv-on-flow tests follavedby en extended build-upin 105 gas wells were available to us. ‘l%ese wellsare spread across 5 major sandstone gas reservoirsof the southern North Sea. The fields are referredto as A, B, C, DandE in Table 1.The values of kh were calculated frun the builduptest and the apparent skin, St, and hence /3 werecalculated fran the drawdowns. The net formationthickness h at a well was estimated fran wirelinelogs. The net reservoir thickness in thesereservoirs was not considered to changesignificantly fran that indicated at a well. Thevalues for porosity and gas saturation are thethickness weighted averages for the cross section-f ~~~ #n.rnmtinn fmInA fpnm tha l-~g~ f~~ ~h~“. .“...1-..”.. *“-..” . . “... . . . .

individual well. Many of the southern North Seagas reservoirs are characterised byahigh liquidsaturation which is inmobile. The values forperforated intervals are subject to someuncertainty since production logs were availablefor less than one thirdof all the wells. For therest, original well canpletion records were used.

SPE 14207 R Nanan , N Shrimanker , J S Archer 3

In some cases the perforated thickness he was foundto be greater than h where the wells were highlydeviated. The relevant data for the five fieldsare given in Table 1. Plots of permeabilityagainst porosity for all the wells are shown in Fig1 and the distribution of data are shown in Fig 2to 4.

uawsuWiCXS

Several different statistical models were tested tofit the observed field data. Both single andmultiple regression methods were used tocorrelate p to other variables as described below.

(a) Linear Regression

The best correlations were obtained when powercurve regression models were used. These are ofthe form

y=cfl (8)

‘i%eywere linearised by taking lcgaritixns

logy= mlogx+c~ (9)

Standard techniques of regressing y on x oralternatively x on y are not applicable in thissituation since errors -are inherent in the~=~~~~~~~~~ of ~~! ~~~ ~~~~Q~~~~= USe of suchstandard methods can lead to erroneous results andcan sanethnes even fail ccnpieteiy. An alternativemethod of minimising the distance perpendicular

from the data point to the regression line8 wasadopted in the present work.

Some of the results found by using the above methodare shmvn in Table 2 along with their correlationcoefficient and standard errors of estimate.

(b) f&iitipie iieg~l?ilshl

Using a straight line regression it is possible totreat only one independent variable at a time. Astandardized multiple regression technique wastherefore used to include more significantvariables. Power curve models were againlinearised for the purpose of regression by takinglogarithms. ~ n~er of

were tested and the bestshuwn in ‘hble 2, Eqn. 19.

~~

Measurements were carried out in the laboratory ona marber of core plugs fran the study fields-andalso from other adjoining fields. The usualprocedure for determining the coefficient ofinertial resistance is to use an integrated form ofEqn 1: which can be expressed10 as

M (p12 -p22 ) wP+ ;

(lo)

2zRTpL(w/A) ‘x

Frana plot of the left hand side against (w/AP)~the value of P can be obtained as the gradient ofthe line and permeability as the inverse of theintercept.

A number of correlations proposed in the literaturehave used the laboratory measured values ofporosity, permeability and p-factors for coreplugs. One of the more reliable empiricalrelationships given by Tek et alll is of the form

5.5 x 109p.

kI.25 90.75

In the presence of an imnobile

this equation could bewritten12

5.5 x 109p=

kl.25 ( q Sg)0.75

Equation lla is dimensionally

(11)

liquid saturation

as

(ha)

inconsistent. Byplotting ? against fl{k, Geertsmaz was able toobtain a straight line from which he proposed adimensionally consistent relation.

48512P = (in field units) (12)

kt).5 9505

In our work measimanents on core plugs were carriedout by flowing gases at increasingly high rates.‘he permeabilities were calculated fran Klinkenbergcorrection plots when the flow rates were lowenough for any inertial effect to be significant.Results of the measurements on 24 core plugs aregiven inTsble 3.

Some of the results obtained from regression arepresented in Figures 5 to 11.The results indicate that an acceptable and usefulcorrelation can be obtained by relating /3 directlyto permeability as shown in Fig 5. ‘l%e lot also

E for ~0~shows lines obtained fran Katz’s equationl-.n~ 9nx pcrog~ty VQ~U~S as well as the lineCL,,” -“-obtained from Geertsmafs relation (Eqn. 12)assuni~ that the porosity is i5%o Iii both eesesit is clear that the existing correlations areunable to predict the observed values withacceptable accuracy. The best fitting straightline is given by ~n. 14. Aplot according to i%n.15 is shown in Fig 6.

The best relationship was obtained when /3 wasrelated to {(k/?.Sg)as shown in Fig 7. This maysuggest that p is directly related to pore geanetrythroughq. The termf(k/q)has been used widely inAL- ,,.- -A..-

+-* fihn~fpterisit’wIne lltehwr~ tiS = ieiiith p~~=~.=. . . . . ., . . . . . ...=

a porous media, eg in Leverett’s “J-function”13 andthis relationship is being explored further by us.According to Eqn. 13, the relationship is alsodimensionally hancgeneous. ‘fhegas saturation termis included since the presence ef a ii~iiid

4 -, Inertial Coefficient in High Rate Gas Wells SPE 14207

saturation will reduce the effective porosity. Inthe present study it has been assumed that theliquid phase present is immobile for all the wells.The liquid production in all cases hardly everexceeded 3-4 bbl/Mvlacf and this is most likely dueto the pressure and temperature change fromwellbore to the surface separators.

l%e experimental results have been plotted in Fig 8using P and k as the axes. The line according toEqn 14 is shown as well as the line of best fitgiven by the dashed line. It can be seen thatEqn.14 can predict the values of pfar better thanexisting relations. The experimental resultsobtained in our laboratory therefore supports thecorrelation derived from field data. Further, theexperimental results show that for l@v permeabilityrocks (ie, 0.1 < k < 1.0 md) the values of ~ maybe at least an order of magnitude higher than thosepredicted by existing correlations.

Plots according to Geertsma’s2 procedure are shownin Fig 9 and 10. A plot of 9 againstp can aiso beused to obtain a very good straight line (Fig 11).However correlations formed fran such plots may beunreliable since the range of porosity data franproducing gas fields are far too narrow to form anyvalid relationship.

It has been suggested14 that the perforatedinterval, he, should be used in Eqn. 5 instead ofthe net formation thickness h. ‘his suggestion isbased on the assumption that non-Darcy flow issignificant only very near to the wellbore. Alsoimplicit is the assumption that the flow iscompletely radial. In this study it was found thatcorrelation coefficients for equations 13 to 19improved considerably when hwes used instead of ~in calculating p from Eqn. 5. The correlationswere also tested for all the data where he WaS lessthen h. It was found that the correlations againimproved by similar mgnitude. ‘l%is suggests thatinertial effects may be significant at largedistances away from the wellbore so that it wouldbe more appropriate to uae h instead of ~. Saneuncertainty is also attached to the values of .

?’In this study production logs were not availab efor most of the wells and evan when available theirinterpretation was ambiguous. In contrast, the netformation thickness can be evaluated with nwchnmrereliability fran wireline logs. The net formationthickness h therefore provides a more reliableparameter to use than hp. For this and the tiovementioned reason only h was used in Eqn. 5 forcalculating P as shown in Table 1. ‘lTie reportedratios betweefi he afid h --- “’” :- %hla 1

cue Uiao ShmTl L1l aa”.= A.

‘lhe permeability near the wellbore is almost alwaysdifferent from the bulk formation permeability duetonmd filtrate invasion, acidising etc. This isalso the region where the non-Darcy effects arenmst significant. It was therefore thought thatthe correlations could be inproved further if )wasrelated to the altered permeability. An equationfor calculating ka, the permeability of the alteredzone has been given by Hawkina15 as

()

ks =_ -lln~ (20)

ka rw

This equation is however not particularly usefulsince ra, the radius of zone of the alteredpermeability is also unknown. By analogy with theconcept of effective wellbore radius14 we canrelate the two pemneabilities.

ka= kexp (-nS)

where n is a constant to be found by trial anderror. A negative skin would thus increase thevalue of ka and a positive skin would have theopposite effect.

Using this method Eqns. 14 and 19 were modified(see Table 2). The improvement in the firstequation was small although in the second case wassignificant. The bulk formation permeabilitytherefore seems to be adequate in formulating thecorrelations especially since inertial effects maybe present at sane distance away fran the wellbore.

‘ine major imitation of the various clorreiati~fi~proposed in this work and by others in theliterature is that only porosity and permeabilityhave been taken as the independent variablescontrolling inertial effects. However, porosityand permeability alone cannot truly characterisethe geanetry of a porous medium surrounding aparticular well. From experimental work we havealso observed that two core plugs having similar

permeabilities can often have markedly differentvalues of the p-factor. It may well be thatalthough permeability is controlled by the narrmvpore throats, the pore sizes or shapes aresufficiently different that the inertial losses atincreasing flmv rates are also quite different.

almlma

1. Data from over one hundred gas wells wereanalysed to obtain the coefficient ofinertial resistance. The coefficients werecorrelated with reservoir parameters. Thesecorrelations, which are supported byexperimental measurements using core plugs,are shown to be better than existingrelations in predicting~.

2. The best correlation canbe formed when p is

;::::e:o($;;o%)‘0.50 This is b~ause the

is a good estimate of themean characteristic iength of a porous media.The relation (Eqn. 13) is dimensionallyhanogeneoua.

3. Correlations according to Geertsma’s methodgive unreliable results since the porosityrange in producing sandstone reservoir rocksis generally narrow.

4. Laboratory measurements of I show that forlav permeability (ie k < 1 md) sandstones,the value of$..can be at leaat an order ofmagnitude higher than those predicted byexistirg correlations.

SPE 14X17 RNanan , N Wn%nanker , J S Archer 5

Correlations were found to be much improvedif p was calculated using the net formationthickness. This is thought to be due tonon-Darcy effects existing at some distanceaway from the wellbQre, we thus find itpreferable to use the net formation thicknessrather than the perforated interval thicknessin Eqn 5.

.A~th~@ it might ha hnttn~ to ~~~=?~ ~ ~~“- “-----

the permeability of the altered zone near thewellbore, the bulk formation permeabilityappears to be adequate for use in predictingthe value of/3

No uniaue correlation could be found forpredicting P fran k and p alone which wouldfit the data perfectly. This is becausep isalso a function of other properties of aporous mediun for which k and P alone provideinadequate description.

NOMENCLATURE

A=A=

B=

D=h =

~= =ke =L=M=m(p)=P=Q=R=ra =re =rw =s=

s’ =Sg .

T=v=w=

z=e=

L! =

Y =

P =

v =

P=

cross sectional area, ft2Darcy coefficient in gas inflow equation,psia21cp/Mscf/dnon-Dercy coefficient in gas inflow equation,DSia2/CD/(MSCf/d)2

The authors would like to thank British GasCorporation (Exploration Department) formaking all the data available to carry outthis study and also for permission to publishthe results. One of the authors (R.N) wouldlike to thank 13X for financial support.

1

2

3

4

5

‘non-b;cy constant in rate dependent skin, l/Mscf/d 6net formation thickness, ftperforated interval thickness, ftbulk formation permeability, mdpermeability of the altered zone near wellbore, mdlength of the flow path, ftmolecular weight of gas, lb/lb mole

real gas pseudo pressure, psia2/cppressure, psiagas flow rate, Macf/duniversal gas constant, ft lbf/lb-mol R

radius of the altered zone near wellbore, ftexternal boundary radius, ftwellbore radius, ftmechanical skin factorrate dependent skingas saturationabsolute temperature, ‘Rfluid velocity, ft/secmass flow rate, lb/seegas compressibility factorcoefficient of viscous flow resistance (=1/k), ft2coefficient of inertial flow resistance, l/ftspecific gravity of gas (air=l.0)density of fluid, lb/cu ftporositygas viscosity, cp

7

8

9

IQ

11

12

13

14

15

Forchheimer, P: Leipzig end Berlin(1914), Chap 15, Sec 116-l!18

Geertsma, J: “Estimating the ~efficient ofInertial Resistance in Fluid Flow ThroughPorous Media”. ~ (Ott 1974), No5, 445.

Firoozabadi, A and Katz, D: ‘An Analysis ofHigh Velocity Gas Flow ’l%rough Porous Median.~ (Feb. 1979), 211

Cornell, D and Katz, D: “Flow of GasesThrough Consolidated Porous Media”,~(Ckt. 1953)S, 2145

Green L and Duwez, P J: “Fluid Flow ’IhroughPorous Metalsn. ~ (1951) la, 39

Mandlebrot, BEk ~LI!l.WHFretmum&Cb, San Francisco (1982)

Alberta Energy Resource Conservation Board:rv... . . . . .

m. Amert, @naaa (i975)o

Dorn, W S and McCrakin, D D:bletbr@ J Wiley & Sons, New York (1972) 357.

Davis, J C: ~. .

GgdrgY, J Wiley and Sons, New York (1973)

Knt.z ~ ~ af ml:..---, Hanrlhook of Natural Gas. .~, McGraw Hill Book Co, New York

(1959).

Tek, M R., Coats, K H and Katz, D Ix TheEffect of Turbulence on Flow of Natural GasThrough Porous Reservoirs”, LEAJl@h (July1962) 799

Ramey, H J: ‘Non-Darcy Flow and WellboreStorage Effects in Pressure Buildup andDrawdown of Gas Wells”, JJ?&ldI, (Feb 1965)223

Leverett, M C: ‘Capillary Behaviour in PorousSolids”, ~,(1941)14i% 153

Dake, L P:~, Elsevier Scientific Publish Co,Amsterdam (1978)

Hawkins, M F: ‘A Note on the Skin Effect”,~(Dec 1956), 65

TABLE 1

Field Data—

Mel 1 hp/h s720. (L) (J) (% (;7

123456

?.99

10111213141516171819202122232425262728293031323334353637383940414243644s

4647486950515253

XIO’3

0.092.154.383.050.58

22.86

10.4511.116

171.15316.207

107.8334.0933.o764.6359.6782.1232.8774.6768.1182.2035.4271.943

12.3892.5646.6762.2072.0731.4432.172

67.7283.0967.8691.9033.1345.793

.7452.4941.420

.2331.1341.6778.600

.256

.916

.276

80.0205.774

14.5082.231

27.839.122

2.92o.686

63.0118.048.0

7.0.90.02.5

13.1064.20

.8816.20

.9612.1022.6025.2012.9027.1068.008.776.60

21.8042.30

202.006.50

121.003.31

23.6028.1028.4022.60

.7410.502.68

14.4065.5051.7089.2024.20

174.00418.WJ104.0068.6042.60

112.00134.0059.10

8.4764.3040.0042.5019.70

606.0068.0082.00

?2tL0 A11.011.710.912.112.911.4

FX72L0B14.112.512.213.114.812.314.113.914.014.419.516.415.713.216.017.915.819.117.015.616.015.715.314.613.411.814.917.616.914.910.118.219.517.017.314.816.015.714.7

nmo c

12.712.613.110.914.617.316.915.5

45.063.052.0SO.o52.053.0

74.069.065.070.071.070.073.072.071.072.068.073.068.071.065.072.o63.066.055.0?5.074.072.070.060.074.050.073.077.079.076.063.077.075.073.073.064.074.075.070.0

60.067. o60.053.059.055.071.036.0

1.01.01.01.01.01.0

.423

.67o

.553

.456

.606

.652

.942

.891

.437

.758

.983

.750

.864

.558

.781

.776

.520

.790

.474

.8051.1951.183

.8611.151

.682

.986

.687

.969

.765

.777

.632

.884

.439

.378

.518

.500

.500

.500

.500

1.0431.0471.0591.052

.8091.110

..913

.474

-4.2-5.0-0.6-3.5-4.0-5.0

0.2-3.7-1.4-3.6-4.0-. 711.9-5.0-2.0-3.8

6.6-2.3-4.7

6.21.8

-6.8-4.4-. 8-2.4-1.44.7

-2.5-3.2-6.3

.9-2.8-3.3-5.0-1.4

.9- .4

8.12.7

-5.0-5.022.04.93.4 ,9.2

-1.85.2

11.9-. 9

1.84.22.0

.9

Wel 1 /9 k 0 hplh s

No. (ft-1) (ad) (x) (3

56’5356575859606162636465666768697071

72737475767778798081828384858687888990919293949596979899

Iw101102103106105

X109

16.299514.85855.896

294.007204.241

96.287131.867295.680

1183.45589.435

305.61578.726

381.026275.941259.516192.393399.592341.779

71.410201.840408.320182.800229.900

12.41024.270

397.42039.090

4.050.92.81052.230

773.62o1739.690

12.18056.760

158.74012.12034.1807.370

87.71013.22018.51025.22019.94020.64042.090

7.340102.040149.51032.170

1.2503.1606.970

71.00.10

4.30.35

1.20.23

6.80.26.06

6.901.236.90

.%!1.10

.601.49.48.38

.91

.88

.28

.52

.5225.80

.54

.733.o25.132.362.16

.50

.234.201.70

.882.553.322.571.516.704.102.804.561.23

.931.70

.54

.651.31

12.6117.606.98

F2EL0 D12.313.613.011.413.712.014.613.213.312.115.513.914.213.815.613.913.311.3

?IELO Iv.14.814.612.914.711.415.412.114.116.617.914.412.412.110.616.616.917.320.217.913.714.816.615.915.813.614.015.616.511.813.410.216.015.015.8

54.061.061.064.058.056.062.041.060.061.062.063.048.048.043.043.048.049.0

57.568.059.956.760.063.454.458.453.862.157.558.656.634.959.961.058.565.965.045.660.866.331.557.345.653.258.960.648.255.833.157.749.257.6

.660

.597

.471

.610

.507

.614

.456

.375

.287

.446

.632

.376

.367

.399

.408

.339

.266

.328

1.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.0

.01-1.80-4.00-1.00

.80- .80

.01- .20-1.20

.01-2.30-2.10- .60

.01-4.10

.01-2.604.00

- .16-3.80-3.50-2.71-3.27- .30-1.70-2.60-2.96

.44-1.37-6.40

.13

.15-1.60-4.60-3.6o-4,30

.90-1.70

.39-2.10-3.40-2.40-3.10-3.50-2.50-2.30-3.90-3.50-1.00- .70-2.70-3.20

.,

TAPLE 2

8SCRESSION EQUATIONS

Correlation Coeff (R)

13qn.

13

14

14a

Refyesslon Squation Standard Error (S)

log P - m 10S (k/ ?. S8)-0-5 + c

n - 2.4388, C - -2.4071

R - 0.9821

logp-mlo~k+c

n = -1.0609, C - 11.0495

R - 0.8883

logp-mlogka+cm - -1.0805, C - 11.0756

ka- k. exp(-o.03s)

R - 0.8903

15

16

17

logp-mlo~(k. ?)+c

m - -1.0356, C - 10.1544

R - O.889S

S - 0.0628

S - i.i9i8

S = 1.4922

Iosq-mloap+cm - -0.0233, C - -0.6068

10s P{k-mlo89+c

m - -30.0799, c - -21.7707

log/3~k - m 10s (P. Sg) + C

n - -13.4639, C - -10.7036

18

19 hO

P“kbl. (?. Sg) b2

bO - 4.7543 X Io10

bl - 0.9212

52 = 0.2429

R - 0.6787

19a bo

P“kbl.(p.so)bz

bO - 1.$633 X lillo

hl - 0.8804

b2 - 0.7770

ka = k. exp(-O.19S)

R - 0.7262

TABLE 3

LABORATORY OATA

J)Sample

No.k

(f t-1.! lo% (d)

1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

M

19

20

21

22

23

24

0.368

14.90

119.0

179.0

17.30

2.021

7.380

7930

1130

0.766

803.031310

1140

42470

17400

865.0

726. o

0.519

1.170

2.010

1.080

0.263

0.636

0.816

59.0

2.180.98

1.23

2.21

17.0

5.900.14

0.23

99.50.41

.041

.260

.064

.102

.460

.515

33.0

15.2

10.5

13.0

32.5

28.4

20.8

20.76

13.8210.19

12.74

12.17

16.92

1.4.90

5.879.96

15.17

7.43

6.8311.39

12.31

11.50

10.01

11.00

21.00

20.50

20.90

23.9o

25.60

19.60

19.01

SPE J 4207

..

“.

. ..”. .

.%”. *.,:.. .

. .%:.s. . . . ... .. ..8... . . “

,.. .e . . .

...-.*“

. ● . .. ..

*. ..”s

s. .

.

.

5 10 Is 20 25 3

I20I

25,

r-n:C

15

F

10

l-l h

li!uM&KPERMEA81LITY [mall

Pis. 2-P91mwUflt% db2rlbuOon of Mn mnP19 set

SPE 1420-7

.

34

10

10’:

10’;

10”

10“

109

108

10’

z‘m.-U.-

:al0u

! I 1 1 1 T

-J

Permeability k (red)

Fb. ~ d @wllh ~MKty.

10’2 1 1~

lo” r❑ 1

❑

10

10

I 09 r 13

I 08 r

110’ F

1067

I 05 1 1

102 103 104 10s 106 10’-0.s

(k/@.Sg) (l/cm)

Fig.7-PM Scm-dng to Sq. !3.

Q

~w.—u.-

=al0u

Permeability . Porosity k~ (red)

Fb, - u=wdlv to Sq. 15.

1510

14

10

~\G ,2

m 10

-E,!’u.- 10”sal:

10i5 10.=

b=

109

108

102 16’ 10° 10’ 102 103 104

Permeability k (red)

Fig. s4Ummlm 0fpflJr*xp9rin18nm dma

SPE 1420-7

L

0 1

162, i , I , i ,

102 103 104 105 106

(3.dkFig. S-Carelatlon bdween q, p, and k.

L +

[

,.’ ~J—————J102 103 104 105 106

./3.dk

Fig. 10-Con’elatlon between r.du~ PCWOSW. i% ad k.

t

-1

0

,~’~ ,,107 108 109 10’0 10” 1012 10

Inertial coefficient @ ( 1 /ft)

Fig. 11-c03mlati0n betwnn portmny ●nd Inwtid cwltlclant.

.SPE 1.4207